First, Kaplan found that average estimated CEO pay, adjusted for inflation, has actually declined since 2000. It's in step with that of lawyers, but CEOs have been out-earned by venture capitalists, private equity executives, and hedge fund managers.

Second, the CEOs who were paid the most had delivered 60 percent greater stock market returns, versus the lowest who underperformed by 20 percent.

Finally, boards fire CEOs at a much greater rate than they used to, and executive tenures are shorter. When boards have larger percentages of equity and independence, bad performance is even more likely to be punished.